CN109388832B - Multi-objective optimization method for power assembly suspension system - Google Patents

Multi-objective optimization method for power assembly suspension system Download PDF

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CN109388832B
CN109388832B CN201710684703.4A CN201710684703A CN109388832B CN 109388832 B CN109388832 B CN 109388832B CN 201710684703 A CN201710684703 A CN 201710684703A CN 109388832 B CN109388832 B CN 109388832B
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吕兆平
李聪
杨玉玲
覃丽霜
秦际宏
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SAIC GM Wuling Automobile Co Ltd
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Abstract

The invention discloses a multi-objective optimization method of a power assembly suspension system. The method comprises the following steps: establishing a dynamic model of a power assembly suspension system; establishing a vibration differential equation of the system on the basis; energy decoupling is carried out on the system by solving the vibration differential equation, so that a dynamic counter force frequency response characteristic function of mass center displacement, rotation angle and suspension of the system is obtained; taking the suspension stiffness and the suspension installation angle as optimization design variables, taking variables such as natural frequency and the like as constraints, taking the maximum energy decoupling rate in the vertical direction and the direction around a crankshaft, the minimum centroid displacement and rotation angle of the system when the centroid of the system loads a unit torque load, and the minimum centroid displacement and rotation angle of the system when the centroid of the system loads a unit displacement load as targets, and establishing a multi-objective function model. According to the invention, the influence of displacement load on the NVH performance of the whole vehicle is considered, and the suspension installation angle is added as an optimization variable, so that a better optimization scheme can be obtained.

Description

Multi-objective optimization method for power assembly suspension system
Technical Field
The invention belongs to the field of automobile structure optimization, and particularly relates to a multi-objective optimization method for a power assembly suspension system.
Background
Currently, in research on automotive engine powertrain suspension systems (including the powertrain and the means to suspend the powertrain), weighted sums of the modal energy decoupling rates of the various orders or portions of the orders are generally targeted at a maximum. Merely taking this as an optimization objective is somewhat ineffective in establishing relationships between the modal capability decouples of each order. In addition, the dynamic response or the vibration transmissibility of the power assembly is minimized, the optimization method ignores the relation between the dynamic state and the static state, and only considers the dynamic response index, so that the optimization result has larger deviation.
The patent of the invention in China with the application number of 201410065485.2 provides a multi-objective optimization method for an engine suspension system. The method is characterized in that the maximum energy decoupling rate in the vertical direction and the minimum amplitude of the sum of the reactive forces of all directions of the four suspensions are taken as targets respectively, the stiffness of all directions of the four suspensions are selected as optimal design variables, the energy decoupling rate constraint around the crankshaft direction and the response constraint of the sum of the reactive torques of all suspensions around the crankshaft are added on the basis of taking the natural frequency, the stiffness of the suspensions and the displacement of the power assembly as constraint conditions, and then the non-dominant ordering genetic algorithm is adopted to carry out multi-target optimization. The method is based on a multi-objective optimization theory, comprehensively considers the energy decoupling dynamic response characteristic of the engine suspension system, takes the energy decoupling dynamic response characteristic as a corresponding optimization objective, and utilizes a multi-objective genetic algorithm to carry out efficient optimization design. The problems are: when the multi-objective optimization function is established, the selected optimization variables do not include the suspension mounting angle, and no load is applied to the system centroid. Because the suspension structure is limited by manufacturing conditions, the optimization variable does not contain a suspension installation angle, and an optimal scheme meeting the manufacturing conditions is not easy to obtain only by taking suspension rigidity as the optimization variable; when the system centroid is not loaded, the influence of NVH (Noise, vibration, harshness, noise, vibration and harshness) performance of different suspension systems on the whole vehicle under idle working conditions and the vibration condition of a seat guide rail on the whole vehicle under starting flameout working conditions cannot be evaluated.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a multi-objective optimization method of a power assembly suspension system.
In order to achieve the above purpose, the invention adopts the following technical scheme:
the invention provides a multi-objective optimization method of a power assembly suspension system, which comprises the following steps:
establishing a dynamic model of a power assembly suspension system;
establishing a vibration differential equation of the system based on the dynamics model;
energy decoupling is carried out on the system by solving the vibration differential equation, so that a dynamic counter force frequency response characteristic function of mass center displacement, rotation angle and suspension of the system is obtained;
the suspension stiffness and the suspension installation angle are used as optimization design variables, and the natural frequency, the suspension stiffness, the mass center displacement, the direction around the crankshaft and the vertical direction (namely the whole vehicle coordinate system G) 0 -xyz, the whole text of which is the same) as constraints, and establishing a multi-objective function model with the maximum energy decoupling rate in the vertical direction and around the crankshaft, the minimum centroid displacement and rotation angle of the system when the centroid of the system is loaded with a unit torque load, and the minimum centroid displacement and rotation angle of the system when the centroid of the system is loaded with a unit displacement load;
and optimizing the multi-objective optimization model by adopting a non-dominant ordering genetic algorithm.
Compared with the prior art, the invention has the following beneficial effects:
the multi-objective optimization function provided by the invention not only considers the influence of the mass center of the system and the torque load, but also considers the influence of the displacement load on the NVH performance of the whole vehicle, and solves the problems that the NVH performance of different suspension systems under the idling working condition of the whole vehicle cannot be evaluated because the displacement load is not added in the prior art, and the vibration condition of the seat guide rail under the starting flameout working condition of the whole vehicle; in the prior art, only the suspension rigidity is used as an optimization variable, and because the suspension structure is limited by manufacturing conditions, an optimal scheme meeting the manufacturing conditions is not easy to obtain. According to the invention, the suspension installation angle is increased to be a second optimization variable, so that a better optimization scheme can be obtained.
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FIG. 1 is a schematic illustration of a kinetic model of a powertrain suspension system constructed in accordance with an embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings.
The embodiment of the invention discloses a multi-objective optimization method of a power assembly suspension system, which comprises the following steps:
step 101, establishing a dynamic model of a power assembly suspension system;
102, establishing a vibration differential equation of the system based on the dynamics model;
step 103, energy decoupling is carried out on the system by solving the vibration differential equation, so as to obtain a dynamic counter force frequency response characteristic function of the centroid displacement, the rotation angle and the suspension of the system when the centroid of the system is loaded with a unit torque load and a unit displacement load respectively;
104, taking the suspension stiffness and the suspension installation angle as optimization design variables, taking any one or more variables of natural frequency, suspension stiffness, mass center displacement of the system and energy decoupling rate around the crankshaft direction and the vertical direction as constraints, taking maximum energy decoupling rate in the vertical direction and around the crankshaft direction, minimum mass center displacement and rotation angle of the system when the mass center of the system loads unit torque load, and minimum mass center displacement and rotation angle of the system when the mass center of the system loads unit displacement load as targets, and establishing a multi-objective function model;
and 105, optimizing the multi-objective optimization model by adopting a non-dominant ranking genetic algorithm.
As an alternative embodiment, the establishing a dynamic model of the suspension system of the power train includes:
as shown in fig. 1, with the centroid G of the system at rest 0 Establishing a three-dimensional rectangular coordinate system G for an origin 0 Xyz (commonly referred to as the whole vehicle coordinate system), the z-axis is vertical and positive upwards when the engine is placed horizontally; the x-axis is in the horizontal plane and is perpendicular to the crankshaft of the engine, and is defined by G 0 The direction pointing to the front end of the engine is the forward direction; the y-axis direction is determined by the right-hand spiral law; at the ith suspension point O i For the origin to pass O i The three mutually perpendicular main stiffness axis directions are the coordinate axis u i 、v i 、w i Establishing a three-dimensional rectangular coordinate system O i -u i v i w i (commonly referred to as an elastic principal axis coordinate system or a local coordinate system), i represents a suspension sequence number, i=1, 2,3, the 1 st suspension is a pre-precursor three-point suspension, the 2 nd suspension is a pre-precursor four-point suspension, and the 3 rd suspension is a pre-precursor post-precursor three-point suspension; the system has 6 degrees of freedom: along three directions of x axis, y axis and z axisAnd (3) moving and rotating around the x axis, the y axis and the z axis.
Centroid G at rest of the system 0 Establishing a three-dimensional rectangular coordinate system G for an origin 0 -xyz, the z-axis being vertical and positive upwards; xG (x G) 0 The y-plane is perpendicular to the z-axis and the x-axis is perpendicular to the crankshaft of the engine, defined by G 0 The direction pointing to the front end of the engine is the forward direction; the y-axis direction is determined by the right-hand spiral law; at the ith suspension point O i For the origin to pass O i The three mutually perpendicular main stiffness axis directions are the coordinate axis u i 、v i 、w i Establishing a three-dimensional rectangular coordinate system O i -u i v i w i I represents a suspension sequence number, i=1, 2 and 3, the 1 st suspension is a front-end precursor three-point suspension, the 2 nd suspension is a front-end precursor four-point suspension, and the 3 rd suspension is a front-end rear-end precursor three-point suspension; the system has 6 degrees of freedom: movement in three directions, x-axis, y-axis, z-axis, rotation about the x-axis, y-axis, z-axis.
It should be noted that the number of suspension points for an automobile is generally 3 or 4, and the suspension system of the present invention employs 3 suspension points. However, the method of the present invention can be adapted to 4 suspension points, with only minor variations.
As an alternative embodiment, the establishing a vibration differential equation of the system based on the dynamics model includes:
and obtaining a vibration differential equation of the system according to the Lagrangian equation and the virtual work principle:
Figure BDA0001376401090000041
in the formula (1), q is a generalized displacement vector, and comprises displacement of the system and corner components rotating around x, y and z directions, F (t) is an exciting force function, and the expression is as follows:
F(t)＝[f x (t),f y (t),f z (t),θ x (t),θ y (t),θ z (t)] T (2)
in the formula (2), t is a time variable, f x (t)、f y (t) and f z (t) is the component of exciting force in x, y and z directions, respectively, θ x (t)、θ y (t) and θ z And (t) is the rotation angle of the exciting force around the x, y and z directions respectively.
In the formula (1), M is a system quality matrix, and the expression is as follows:
Figure BDA0001376401090000051
in the formula (3), m is the total mass of the system, I xx 、I yy 、I zz Moment of inertia of the system about the x-axis, y-axis, z-axis, respectively, I xy And I yx 、I yz And I zy 、I zx And I xz Respectively, the system is at xG 0 y plane, yG 0 z-plane and zG 0 The product of inertia of the x plane and satisfies I xy ＝I yx ，I yz ＝I zy ，I zx ＝I xz ；
In the formula (1), C is a system damping matrix, and the expression is as follows:
Figure BDA0001376401090000052
in the formula (4), c xx 、c yy 、c zz Component of total reciprocation damping of elastic support in x, y and z directions c αα 、c ββ 、c γγ Is the component of the total rotational damping of the elastic support about the x, y, z directions.
In the formula (1), K is a system stiffness matrix, and the expression is:
Figure BDA0001376401090000053
in the formula (5), D i For the local stiffness matrix of the system of the ith suspension, D i The expression of (2) is:
Figure BDA0001376401090000054
in the formula (6), K ui 、K vi 、K wi The main rigidity of the ith suspension in the u, v and w directions is respectively;
in the formula (5), B i The directional cosine matrix for the ith suspension is expressed as follows:
Figure BDA0001376401090000061
in the formula (7), alpha 1i 、α 2i 、α 3i U respectively i Included angle between positive axis and positive x, y and z axes, beta 1i 、β 2i 、β 3i V respectively i Included angle between positive axis and positive x, y and z axes, gamma 1i 、γ 2i 、γ 3i W is respectively i Included angles between the positive axis direction and positive x, y and z axes;
in the formula (5), E i To be from O i -u i v i w i Coordinate system to G 0 -a position transformation matrix of an xyz coordinate system, expressed as:
Figure BDA0001376401090000062
in the formula (8), (x) i ,y i ,z i ) Is O i -u i v i w i Origin of coordinate system O i At G 0 -coordinates in xyz coordinate system.
As an optional embodiment, the step of performing energy decoupling on the system by solving the vibration differential equation to obtain a dynamic counter force frequency response characteristic function of the centroid displacement, the rotation angle and the suspension of the system specifically includes:
solving the vibration differential equation by using a modal decoupling method: assuming that the system vibrates slightly, neglecting the damping effect, the vibration differential equation of the system is simplified by equation (1):
Figure BDA0001376401090000063
when F (t) is a sine function with frequency ω (to be precise, ω is an angular frequency, here simply referred to as frequency, the same applies below), that is, in the case of sinusoidal excitation, the solution of equation (9) is:
Figure BDA0001376401090000064
in the formula (10), t is a time variable, X is an amplitude value, and alpha is a phase angle;
when the system vibrates with the ith order of primary vibration, the percentage of energy allocated in the kth degree of freedom to the total energy of the system is:
Figure BDA0001376401090000065
in the formula (11), m kl K row/column element of M;
Figure BDA0001376401090000071
respectively the i-th order main mode of the system +.>
Figure BDA0001376401090000072
The kth element and the first element,/-, of (a)>
Figure BDA0001376401090000073
Tp ki The greater the value, the higher the degree of decoupling is for the energy decoupling rate.
The suspension point of the ith suspension is G 0 Displacement U in xyz coordinate system i ' with it at O i -u i v i w i Displacement U in a coordinate system i And the centroid displacement q of the system is:
U i '＝[I-r i ]q＝B i U i (12)
in the formula (12), I is a 3×3-order identity matrix, r i Is the ith suspensionThe suspension point is G 0 3X 3-order oblique symmetry matrix composed of coordinates in xyz coordinate system (which is exactly E i A matrix of 3 columns to the right).
When the ground has vertical displacement excitation z (t), the displacement of the suspension points of each suspension is the same as the excitation displacement of the ground, the ith suspension is arranged at O i -u i v i w i Force f in coordinate system i The method comprises the following steps:
f i ＝K i (U i -U ig ) (13)
in the formula (13), U ig Suspension point for the ith suspension at O i -u i v i w i Displacement in a coordinate system, an
Figure BDA0001376401090000074
U' ig Suspension point for the ith suspension at G 0 Displacement in xyz coordinate system, and U' ig T ＝{0,0,z(t)}；K i For the ith suspension at O i -u i v i w i The complex stiffness matrix under the coordinate system has the expression:
Figure BDA0001376401090000075
in the formula (14), K' ui +jK” ui 、K' vi +jK” vi 、K' wi +jK” wi Respectively the ith suspension at u i 、v i 、w i Complex stiffness in three directions.
Will f i Conversion to G 0 Force F in xyz coordinate system i ：
Figure BDA0001376401090000076
The generalized total force matrix EFM comprising moment components, which is acted on the system by the 3 suspension points, is obtained by solving the counterforce and counter moment of the supporting points on the system, wherein the generalized total force matrix EFM comprises the moment components and is:
Figure BDA0001376401090000081
in the formulas (15) and (16), the symbol "indicates that the conjugate is taken.
According to Newton's second law:
Figure BDA0001376401090000082
in the formula (17), EF is a generalized external force matrix including external moment components acting on the system, and mainly includes a force in a vertical direction and a moment in a direction around the crankshaft.
Substituting formula (16) into formula (17):
Figure BDA0001376401090000083
the centroid displacement and corner frequency response characteristics of the system are as follows:
q(f)＝(-Mω 2 +K) -1 [F(f)+EF(f)] (19)
in the formula (19), f is a frequency variable; f (F) =0 when excitation of the road surface is not considered; EF (f) =0 when only excitation of the road surface is considered.
The ith suspension of the system is G 0 The frequency response characteristic of the dynamic reaction force in the xyz coordinate system can be obtained by the equation (15).
As an optional embodiment, the building the multi-objective optimization model specifically includes:
with maximum energy decoupling rate in the vertical direction and the direction around the crankshaft as the first optimized objective function f 1 (d) To shift the centre of mass of the system and to turn the angle q when the centre of mass of the system is loaded with a unit torque load 1 (f) (obtained by equation (19)) minimum as the second optimization objective function f 2 (d) To provide a centroid displacement and a rotation angle q of the system when the centroid of the system is loaded with a unit displacement load 2 (f) (obtained by equation (19)) minimum as a third optimization objective function f 3 (d) Establishing a targetFunction f 0 (d) The model of (2) is as follows:
Figure BDA0001376401090000091
in the formula (20), D is an optimal design variable, and D is D i And B i ；δ i A weighting factor for the i-th order natural frequency; s.t. (natural frequency, suspension stiffness, mass center displacement of the system, energy decoupling rate around the crankshaft direction and vertical direction) represents constraint with any one or several variables of natural frequency, suspension stiffness, mass center displacement of the system, energy decoupling rate around the crankshaft direction and vertical direction.
The foregoing description of the embodiments of the present invention should not be taken as limiting the scope of the invention, but rather should be construed as falling within the scope of the invention, as long as the invention is modified or enlarged or reduced in terms of equivalent variations or modifications, equivalent proportions, or the like, which are included in the spirit of the invention.

Claims (4)

1. A method of multi-objective optimization of a powertrain suspension system, comprising:
establishing a dynamic model of a power assembly suspension system;
establishing a vibration differential equation of the system based on the dynamics model;
energy decoupling is carried out on the system by solving the vibration differential equation, so that a dynamic counter force frequency response characteristic function of mass center displacement, rotation angle and suspension of the system is obtained; executing the specific steps of solving the vibration differential equation, and performing energy decoupling on the system to obtain the dynamic counter force frequency response characteristic functions of mass center displacement, rotation angle and suspension of the system, wherein the specific steps are as follows:
solving the vibration differential equation by using a modal decoupling method: assuming that the system vibrates slightly, neglecting the damping effect, the vibration differential equation of the system is simplified by equation (1):
Figure FDA0004172267240000011
when F (t) is a sine function with the frequency omega, solving the equation (9) to obtain:
Figure FDA0004172267240000012
in the formula (10), t is a time variable, X is an amplitude value, and alpha is a phase angle;
when the system vibrates with the ith order of principal vibration, the percentage of energy allocated to the kth degree of freedom in the total energy of the system is:
Figure FDA0004172267240000013
in the formula (11), m kl K row/column element of M;
Figure FDA0004172267240000014
respectively the i-th order main mode of the system +.>
Figure FDA0004172267240000015
The kth element and the first element,/-, of (a)>
Figure FDA0004172267240000016
Tp ki The greater the value of the energy decoupling rate, the higher the degree of decoupling;
the suspension point of the ith suspension is G 0 Displacement U in xyz coordinate system i ' with it at O i -u i v i w i Displacement U in a coordinate system i And the centroid displacement q of the system is:
U′ i ＝[I-r i ]q＝B i U i (12)
in the formula (12), I is a 3×3-order identity matrix, r i Suspension point for the ith suspension at G 0 Coordinate composition in an xyz coordinate system3 x 3 order oblique symmetry matrix of (2);
when the ground has vertical displacement excitation z (t), the displacement of the suspension points of each suspension is the same as the excitation displacement of the ground, the ith suspension is arranged at O i -u i v i w i Force f in coordinate system i The method comprises the following steps:
f i ＝K i (U i -U ig ) (13)
in the formula (13), U ig Suspension point for the ith suspension at O i -u i v i w i Displacement in a coordinate system, an
Figure FDA0004172267240000021
U′ ig Suspension point for the ith suspension at G 0 -displacement in xyz coordinate system, and +.>
Figure FDA0004172267240000022
K i For the ith suspension at O i -u i v i w i The complex stiffness matrix under the coordinate system has the expression:
Figure FDA0004172267240000023
in the formula (14), K' ui +jK″ ui 、
Figure FDA0004172267240000024
K' wi +jK″ wi Respectively the ith suspension at u i 、v i 、w i Complex stiffness in three directions;
will f i Conversion to G 0 Force F in xyz coordinate system i ：
Figure FDA0004172267240000025
The generalized total force matrix EFM comprising moment components, which is acted on the system by the 3 suspension points, is obtained by solving the counterforce and counter moment of the supporting points on the system, wherein the generalized total force matrix EFM comprises the moment components and is:
Figure FDA0004172267240000026
in the formulas (15), (16), "×" represents conjugation;
according to Newton's second law:
Figure FDA0004172267240000027
in the formula (17), EF is a generalized external force matrix containing external moment components and acting on the system, and mainly comprises force in the vertical direction and moment in the direction around a crankshaft;
substituting formula (16) into formula (17):
Figure FDA0004172267240000031
the centroid displacement and corner frequency response characteristics of the system are as follows:
q(f)＝(-Mω 2 +K) -1 [F(f)+EF(f)] (19)
in the formula (19), f is a frequency variable; f (F) =0 when excitation of the road surface is not considered; EF (f) =0 when only excitation of the road surface is considered;
the ith suspension of the system is G 0 The frequency response characteristic of the dynamic reaction force in the xyz coordinate system can be obtained by the formula (15);
taking the suspension stiffness and the suspension installation angle as optimal design variables, taking any one or more variables of natural frequency, suspension stiffness, mass center displacement of the system and energy decoupling rate around the crankshaft direction and the vertical direction as constraints, taking maximum energy decoupling rate in the vertical direction and around the crankshaft direction, minimum mass center displacement and rotation angle of the system when the mass center of the system loads unit torque load, and minimum mass center displacement and rotation angle of the system when the mass center of the system loads unit displacement load as targets, and establishing a multi-objective function model;
and optimizing the multi-objective function model by adopting a non-dominant ordering genetic algorithm.
2. The powertrain suspension system multi-objective optimization method of claim 1, wherein the modeling of dynamics of the powertrain suspension system comprises:
centroid G at rest of the system 0 Establishing a three-dimensional rectangular coordinate system G for an origin 0 -xyz, the z-axis being vertical and positive upwards when the engine is placed horizontally; the x-axis is in the horizontal plane and is perpendicular to the crankshaft of the engine, and is defined by G 0 The direction pointing to the front end of the engine is the forward direction; the y-axis direction is determined by the right-hand spiral law; at the ith suspension point O i For the origin to pass O i The three mutually perpendicular main stiffness axis directions are the coordinate axis u i 、v i 、w i Establishing a three-dimensional rectangular coordinate system O i -u i v i w i I represents a suspension sequence number, i=1, 2 and 3, the 1 st suspension is a front-end precursor three-point suspension, the 2 nd suspension is a front-end precursor four-point suspension, and the 3 rd suspension is a front-end rear-end precursor three-point suspension; the system has 6 degrees of freedom: movement in three directions, x-axis, y-axis, z-axis, rotation about the x-axis, y-axis, z-axis.
3. The powertrain suspension system multi-objective optimization method of claim 2, wherein the establishing a vibration differential equation of the system based on the dynamics model comprises:
and obtaining a vibration differential equation of the system according to the Lagrangian equation and the virtual work principle:
Figure FDA0004172267240000041
in the formula (1), q is a generalized displacement vector, and comprises displacement of the system and corner components rotating around x, y and z directions, F (t) is an exciting force function, and the expression is as follows:
F(t)＝[f x (t),f y (t),f z (t),θ x (t),θ y (t),θ z (t)] T (2)
in the formula (2), t is a time variable, f x (t)、f y (t) and f z (t) is the component of exciting force in x, y and z directions, respectively, θ x (t)、θ y (t) and θ z (t) are the corners of the exciting force around the x, y and z directions respectively;
in the formula (1), M is a system quality matrix, and the expression is as follows:
Figure FDA0004172267240000042
in the formula (3), m is the total mass of the system, I xx 、I yy 、I zz Moment of inertia of the system about the x-axis, y-axis, z-axis, respectively, I xy And I yx 、I yz And I zy 、I zx And I xz Respectively, the system is at xG 0 y plane, yG 0 z-plane and zG 0 The product of inertia of the x plane and satisfies I xy ＝I yx ，I yz ＝I zy ，I zx ＝I xz ；
In the formula (1), C is a system damping matrix, and the expression is as follows:
Figure FDA0004172267240000043
in the formula (4), c xx 、c yy 、c zz Component of total reciprocation damping of elastic support in x, y and z directions c αα 、c ββ 、c γγ Components around x, y, z directions of the total rotational damping of the elastic support;
in the formula (1), K is a system stiffness matrix, and the expression is:
Figure FDA0004172267240000051
in the formula (5), D i For the local stiffness matrix of the system of the ith suspension, D i The expression of (2) is:
Figure FDA0004172267240000052
in the formula (6), K ui 、K vi 、K wi The main rigidity of the ith suspension in the u, v and w directions is respectively;
in the formula (5), B i The directional cosine matrix for the ith suspension is expressed as follows:
Figure FDA0004172267240000053
in the formula (7), alpha 1i 、α 2i 、α 3i U respectively i Included angle between positive axis and positive x, y and z axes, beta 1i 、β 2i 、β 3i V respectively i Included angle between positive axis and positive x, y and z axes, gamma 1i 、γ 2i 、γ 3i W is respectively i Included angles between the positive axis direction and positive x, y and z axes;
in the formula (5), E i To be from O i -u i v i w i Coordinate system to G 0 -a position transformation matrix of an xyz coordinate system, expressed as:
Figure FDA0004172267240000054
in the formula (8), (x) i ,y i ,z i ) Is O i -u i v i w i Origin of coordinate system O i At G 0 -coordinates in xyz coordinate system.
4. The method of claim 1, wherein the building a multi-objective function model specifically comprises:
with maximum energy decoupling rate in the vertical direction and the direction around the crankshaft as the first optimized objective function f 1 (d) To shift the centre of mass of the system and to turn the angle q when the centre of mass of the system is loaded with a unit torque load 1 (f) Minimum as second optimization objective function f 2 (d) To provide a centroid displacement and a rotation angle q of the system when the centroid of the system is loaded with a unit displacement load 2 (f) Minimum as third optimization objective function f 3 (d) Establishing an objective function f 0 (d) The model of (2) is as follows:
Figure FDA0004172267240000061
in the formula (20), D is an optimal design variable, and D is D i And B i ；δ i A weighting factor for the i-th order natural frequency; s.t. (natural frequency, suspension stiffness, mass center displacement of the system, energy decoupling rate around the crankshaft direction and vertical direction) represents constraint with any one or several variables of natural frequency, suspension stiffness, mass center displacement of the system, energy decoupling rate around the crankshaft direction and vertical direction.
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